Julian Day

Converts Gregorian calendar and Julian dates. Based on a TI-59 program by Charles Kluepfel.

This program converts dates between the Gregorian calendar and Julian Day Numbers, a continuous count of days used in astronomy. It accepts input in either direction: a calendar date (month, day, year, and AD/BC era) to its Julian Day Number, or a Julian Day Number back to a calendar date. The Gregorian-to-Julian conversion handles the BC/AD era transition by negating and shifting the year, and corrects for century leap-year irregularities using the standard INT(Y/100) adjustment. A shared subroutine at line 4000 performs the repeated division-with-remainder operations needed during the reverse (JD-to-date) conversion. The day-of-week calculation uses a fractional-part trick on (JD+1)/7 to map the Julian Day Number to a named weekday.

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Program Structure

The program is divided into clearly labelled sections using REM blocks. Control flow is menu-driven from line 110, branching to one of two main routines:

1. Lines 1000–2230: Gregorian date → Julian Day Number, followed by day-of-week display, then looping back to line 1000.
2. Lines 3000–3170: Julian Day Number → Gregorian date, looping back to line 3000.
3. Lines 4000–4090: Shared subroutine used three times during JD-to-date conversion.

Both main routines loop indefinitely (GO TO 1000 at line 2230, GO TO 3000 at line 3170), requiring a BREAK to exit. There is no unified main loop or return-to-menu option after either calculation path is entered.

Gregorian-to-Julian Conversion (Lines 2000–2150)

The algorithm follows the standard astronomical formula, ported from a TI-59 program by Charles Kluepfel (1978). Key steps:

• Months January and February are treated as months 13 and 14 of the previous year (lines 2015–2020), a standard technique that simplifies the 30.6-day month-length formula.
• For BC years, the astronomical year numbering convention is applied at line 1045: Y = -(Y-1), mapping 1 BC → 0, 2 BC → −1, etc.
• Negative years trigger a 400-year block alignment at lines 2055–2070, accumulating a correction in J and shifting Y into a non-negative range before the main formula runs.
• The Gregorian century correction is INT(Y/100) scaled by 0.75 and subtracted at line 2130, implementing the standard -INT(A/100)+INT(A/400)+2 correction folded into the constant 1721060.

A notable oddity is the use of DIS at lines 2140–2150: it is set to JD (which is 0 at this point), then JD is set to J, and DIS = J - 0, so the display value always equals J. This appears to be a vestige of a more general accumulation pattern from the original calculator program.

Julian-Day-to-Gregorian Conversion (Lines 3000–3170)

This section calls the subroutine at line 4000 three times to successively extract the year century, year within century, and month. The logic relies on a shared register protocol using T, DIS, XT, and SAVE:

Call	DIS (divisor)	Purpose
1st (line 3030)	36524.25	Extract century count → contributes to Y
2nd (line 3060)	365.25	Extract year within century → adds to Y
3rd (line 3105)	30.6	Extract month number → sets M

After the third call, a swap at line 3120 puts the day remainder into DIS and D = DIS + 1 at line 3130. The month adjustment for January/February (adding back the 12 offset) is at lines 3140–3150, and BC conversion at line 3155 using ABS Y + 1.

Shared Subroutine (Lines 4000–4090)

The subroutine performs an integer division of T by DIS, returning the quotient in J and the remainder (scaled back to the original units) in T. It uses a swap idiom with XT as a temporary register since the platform lacks multi-variable swap syntax. Key steps:

• Line 4010: Swaps DIS and T; saves original DIS into J and pre-computes SAVE = DIS + 0.9.
• Lines 4030–4032: Computes DIS = INT((DIS+0.9)/T), with a correction +1 if negative before truncation — handling negative-year edge cases.
• Line 4050: Computes remainder as SAVE - quotient * original_divisor.
• Lines 4070–4071: Applies the same negative-integer floor correction to the remainder T.

The +0.9 bias before INT is used in place of rounding, since the inputs are not exact integers due to floating-point intermediate values.

Day-of-Week Calculation

Lines 2210–2227 use a fractional-part technique: (JD+1)/7 - INT((JD+1)/7) gives the fractional day position within a week cycle, then INT(7*frac + 1.5) maps it to an integer 1–7. Seven consecutive IF statements print the named weekday. This is slightly inefficient but clear; a DATA/array approach was not available in standard Sinclair BASIC of this era.

Notable Bugs and Anomalies

• Line 20’s REM says “CALENDER” (misspelling of “calendar”) — a cosmetic issue only.
• The variable SAVE used in the subroutine (line 4010) is not declared in the variable list in the REM at lines 30–31, suggesting it was added during porting.
• The menu at line 110 does not validate input beyond checking for 0 or 1; any other value causes the program to fall through both IF checks and re-display the PRINT AT line from line 100, effectively looping but without re-prompting cleanly.
• Line 3080 adds 91.4 to T, which is a fixed offset used in month extraction; this is a direct translation of the TI-59 register arithmetic and works correctly but is not self-documenting.
• The © = RESET keyword in the title REM at line 10 is the TS2068 RESET token, used here as part of the copyright symbol in the author credit — a coincidence of character encoding.